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SUMMARY:Sean Howe (University of Utah)
DTSTART:20210513T210000Z
DTEND:20210513T220000Z
DTSTAMP:20260423T022810Z
UID:UCSD_NTS/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/37/
 ">Bialgebraicity in local Shimura varieties</a>\nby Sean Howe (University 
 of Utah) as part of UCSD number theory seminar\n\nLecture held in normally
  APM 7321\, currently online.\n\nAbstract\nA classical transcendence resul
 t of Schneider on the modular $j$-invariant states that\, for $\\tau \\in 
 \\mathbb{H}$\, both $\\tau$ and $j(\\tau)$ are in $\\overline{\\mathbb{Q}}
 $ if and only if $\\tau$ is contained in an imaginary quadratic extension 
 of $\\mathbb{Q}$. The space $\\mathbb{H}$ has a natural interpretation as 
 a parameter space for $\\mathbb{Q}$-Hodge structures (or\, in this case\, 
 elliptic curves)\, and from this perspective the imaginary quadratic point
 s are distinguished as corresponding to objects with maximal symmetry. Thi
 s result has been generalized by Cohen and Shiga-Wolfart to more general m
 oduli of Hodge structures (corresponding to abelian-type Shimura varieties
 )\, and by Ullmo-Yafaev to higher dimensional loci of extra symmetry (spec
 ial subvarieties)\, where bialgebraicity is intimately connected with the 
 Pila-Zannier approach to the Andre-Oort conjecture.\n\nIn this talk\, I wi
 ll discuss work in progress with Christian Klevdal on an analogous bialgeb
 raicity characterization of special subvarieties in Scholze's local Shimur
 a varieties and more general diamond moduli of $p$-adic Hodge structures.\
 n\nThere will be a pretalk!\n\npre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/37/
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